Abstract-In this paper propagation losses of body implanted antennas are studied at the ISM bands of 433 MHz, 915 MHz, 2450 MHz and 5800 MHz. Two body models are used, one based on a single equivalent layer and the other based on a three layer structure, showing the advantages and limitations of each one. Firstly, the antenna pair gain at different implanted antenna depths is analyzed. Next, we show the effects of the thickness of the different body tissue layers. Finally, we discuss the consequences of using a coating layer to isolate the antenna from the harsh environment of the human body.

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Abstract-For electromagnetic analysis using Method of Moments (MoM), three-dimensional (3-D) arbitrary conducting surfaces are often discretized in Rao, Wilton and Glisson basis functions. The MoM Galerkin discretization of the magnetic field integral equation (MFIE) includes a factor 0 equal to the solid angle external to the surface at the testing points, which is 2 everywhere on the surface of the object, except at edges or tips that constitute a set of zero measure. However, the standard formulation of the MFIE with 0 = 2 leads to inaccurate results for electrically small sharp-edged objects. This paper presents a correction to the 0 factor that, using Galerkin testing in the MFIE, gives accuracy comparable to the electric field integral equation (EFIE), which behaves very well for small sharp-edged objects and can be taken as a reference.

The multilevel matrix decomposition algorithm (MLMDA) was originally developed by Michielsen and Boag for 2-D TMz scattering problems and later implemented in 3-D by Rius et al. The 3-D MLMDA was particularly efficient and accurate for piece-wise planar objects such as printed antennas. However, for arbitrary 3-D problems it was not as efficient as the multilevel fast multipole algorithm (MLFMA) and the matrix compression error was too large for practical applications. This paper will introduce some improvements in 3-D MLMDA, like new placement of equivalent functions and SVD postcompression. The first is crucial to have a matrix compression error that converges to zero as the compressed matrix size increases. As a result, the new MDA-SVD algorithm is comparable with the MLFMA and the adaptive cross approximation (ACA) in terms of computation time and memory requirements. Remarkably, in high-accuracy computations the MDA-SVD approach obtains a matrix compression error one order of magnitude smaller than ACA or MLFMA in less computation time. Like the ACA, the MDA-SVD algorithm can be implemented on top of an existing MoM code with most commonly used Green's functions, but the MDA-SVD is much more efficient in the analysis of planar or piece-wise planar objects, like printed antennas. Index Terms-Fast integral equation methods, method of moments (MoM), multilayer Green's function, printed antennas.

The multilevel matrix decomposition algorithm (MLMDA) has been implemented in 3‐D for the solution of large electromagnetic problems. The electric field integral equation is solved for arbitrary surfaces discretized using N Rao, Wilton, and Glisson basis functions. The MLMDA accelerates the matrix–vector products in a conjugate gradient or biconjugate gradient iterative solution of the resulting system of equations. The computational cost of each iteration is proportional to N log2 N for very large problems, and is particularly small for planar or piecewise planar objects. ©1999 John Wiley & Sons, Inc. Microwave Opt Technol Lett 22: 177–182, 1999.

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The application of integral equation methods based in the method of moments discretization to solve large antenna arrays is difficult due to the fact that the computational requirements increase rapidly with the number of unknowns. This is critical when a frequency analysis of the antenna is required. We propose the multilevel matrix decomposition algorithm (MLMDA) to carry out this purpose efficiently. As the MLMDA method is particularly well-suited for the analysis of planar structures with any Green's function, it is a very efficient approach for the frequency analysis of microstrip antenna arrays.

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